δος μοι που στω και κινω την γην — Dos moi pou sto kai kino taen gaen (in epigram form, as given by Pappus, classical Greek).δος μοι πα στω και τα γαν κινάσω — Dos moi pa sto kai tan gan kinaso (Doric Greek).Give me a place to stand on and I can move the Earth.About four centuries before Pappas, but about three centuries after Archimedes lived, Plutarch had written of Archimedes' understanding of the lever:Archimedes, a kinsman and friend of King Hiero, wrote to him that with a given force, it was possible to move any given weight; and emboldened, as it is said, by the strength of the proof, he asserted that, if there were another world and he could go to it, he would move this one.A commonly-seen expanded variation of the aphorism is:Give me a lever long enough and a place to stand, and I can move the earth.

As attributed to Pappus (4th century A.D.) and Plutarch (c. 46-120 A.D.), in Sherman K. Stein, Archimedes: What Did He Do Besides Cry Eureka? (1999), 5, where it is also stated that Archimedes knew that ropes and pulley exploit “the principle of the lever, where distance is traded for force.” Eduard Jan Dijksterhuis, in his book, Archimedes (1956), Vol. 12., 15. writes that Hiero invited Archimedes to demonstrate his claim on a ship from the royal fleet, drawn up onto land and there loaded with a large crew and freight, and Archimedes easily succeeded. Thomas Little Heath in The Works of Archimedes (1897), xix-xx, states according to Athenaeus, the mechanical contrivance used was not pulleys as given by Plutarch, but a helix., Heath provides cites for Pappus Synagoge, Book VIII, 1060; Plutarch, Marcellus, 14; and Athenaeus v. 207 a-b. What all this boils down to, in the opinion of the Webmaster, is the last-stated aphorism would seem to be not the actual words of Archimedes (c. 287 – 212 B.C.), but restatements of the principle attributed to him, formed by other writers centuries after his lifetime.

I believe in logic, the sequence of cause and effect, and in science its only begotten son our law, which was conceived by the ancient Greeks, thrived under Isaac Newton, suffered under Albert Einstein…That fragment of a 'creed for materialism' which a friend in college had once shown him rose through Donald's confused mind.

A chemical name should not be a phrase, it ought not to require circumlocutions to become definite; it should not be of the type “Glauber’s salt”, which conveys nothing about the composition of the substance; it should recall the constituents of a compound; it should be non-committal if nothing is known about the substance; the names should preferably be coined from Latin or Greek, so that their meaning can be more widely and easily understood; the form of the words should be such that they fit easily into the language into which they are to be incorporated.

Although I was four years at the University [of Wisconsin], I did not take the regular course of studies, but instead picked out what I thought would be most useful to me, particularly chemistry, which opened a new world, mathematics and physics, a little Greek and Latin, botany and and geology. I was far from satisfied with what I had learned, and should have stayed longer.[Enrolled in Feb 1861, left in 1863 without completing a degree, and began his first botanical foot journey.]

And for rejecting such a Medium, we have the Authority of those the oldest and most celebrated Philosophers of Greece and Phoenicia, who made a Vacuum, and Atoms, and the Gravity of Atoms, the first Principles of their Philosophy; tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phaenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical; and not only to unfold the Mechanism of the World, but chiefly to resolve these and such like Questions. What is there in places almost empty of Matter, and whence is it that the Sun and Planets gravitate towards one another, without dense Matter between them? Whence is it that Nature doth nothing in vain; and whence arises all that Order and Beauty which we see in the World? ... does it not appear from phaenomena that there is a Being incorporeal, living, intelligent, omnipresent, who in infinite space, as it were in his Sensory, sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself.

In Opticks, (1704, 2nd. Ed. 1718), Book 3, Query 28, 343-5. Newton’s reference to “Nature does nothing in vain” recalls the axiom from Aristotle, which may be seen as “Natura nihil agit frustra” in the Aristotle Quotes on this web site.

Aristotle’s opinion … that comets were nothing else than sublunary vapors or airy meteors … prevailed so far amongst the Greeks, that this sublimest part of astronomy lay altogether neglected; since none could think it worthwhile to observe, and to give an account of the wandering and uncertain paths of vapours floating in the Ether.

Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world could have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility. … Our modern power of easy reckoning with decimal fractions is the most miraculous result of a perfect notation.

But although in theory physicists realize that their conclusions are ... not certainly true, this ... does not really sink into their consciousness. Nearly all the time ... they ... act as if Science were indisputably True, and what's more, as if only science were true.... Any information obtained otherwise than by the scientific method, although it may be true, the scientists will call “unscientific,” using this word as a smear word, by bringing in the connotation from its original [Greek] meaning, to imply that the information is false, or at any rate slightly phony.

Development of Western science is based on two great achievements: the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance). In my opinion, one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.

Early Greek astronomers, derived their first knowledge from the Egyptians, and these from the Chaldeans, among whom the science was studied, at a very early period. Their knowledge of astronomy, which gave their learned men the name of Magi, wise men, afterwards degenerated into astrology, or the art of consulting the position of the stars to foretel events—and hence sprung the silly occupation of sooth saying, for which the Chaldeans were noted to a proverb, in later ages.

Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.

From very ancient times, the question of the constitution of matter with respect to divisibility has been debated, some adopting the opinion that this divisibility is infinite …. We have absolutely no means at our disposal for deciding such a question, which remains at the present day in the same state as when it first engaged the attention of the Greek philosophers, or perhaps that of the sages of Egypt and Hindostan long before them.

In Elementary Chemistry, Theoretical and Practical (1854), 206. Note: this was the limit of knowledge, or even speculation, decades before the discovery of the nucleus, electron, proton and other particles.

Hieron asked Archimedes to discover, without damaging it, whether a certain crown or wreath was made of pure gold, or if the goldsmith had fraudulently alloyed it with some baser metal. While Archimedes was turning the problem over in his mind, he chanced to be in the bath house. There, as he was sitting in the bath, he noticed that the amount of water that was flowing over the top of it was equal in volume to that part of his body that was immersed. He saw at once a way of solving the problem. He did not delay, but in his joy leaped out of the bath. Rushing naked through the streets towards his home, he cried out in a loud voice that he had found what he sought. For, as he ran, he repeatedly shouted in Greek; “Eureka! Eurekal I’ve found it! I’ve found it!”

Historically [chemistry] arose from a constellation of interests: the empirically based technologies of early metallurgists, brewers, dyers, tanners, calciners and pharmacists; the speculative Greek philosphers' concern whether brute matter was invariant or transformable; the alchemists' real or symbolic attempts to achieve the transmutation of base metals into gold; and the iatrochemists' interst in the chemistry and pathology of animal and human functions. Partly because of the sheer complexity of chemical phenomena, the absence of criteria and standards of purity, and uncertainty over the definition of elements ... but above all because of the lack of a concept of the gaseous state of matter, chemistry remained a rambling, puzzling and chaotic area of natural philosophy until the middle of the eighteenth century.

I cannot find anything showing early aptitude for acquiring languages; but that he [Clifford] had it and was fond of exercising it in later life is certain. One practical reason for it was the desire of being able to read mathematical papers in foreign journals; but this would not account for his taking up Spanish, of which he acquired a competent knowledge in the course of a tour to the Pyrenees. When he was at Algiers in 1876 he began Arabic, and made progress enough to follow in a general way a course of lessons given in that language. He read modern Greek fluently, and at one time he was furious about Sanskrit. He even spent some time on hieroglyphics. A new language is a riddle before it is conquered, a power in the hand afterwards: to Clifford every riddle was a challenge, and every chance of new power a divine opportunity to be seized. Hence he was likewise interested in the various modes of conveying and expressing language invented for special purposes, such as the Morse alphabet and shorthand. … I have forgotten to mention his command of French and German, the former of which he knew very well, and the latter quite sufficiently; …

I cannot serve as an example for younger scientists to follow. What I teach cannot be learned. I have never been a “100 percent scientist.” My reading has always been shamefully nonprofessional. I do not own an attaché case, and therefore cannot carry it home at night, full of journals and papers to read. I like long vacations, and a catalogue of my activities in general would be a scandal in the ears of the apostles of cost-effectiveness. I do not play the recorder, nor do I like to attend NATO workshops on a Greek island or a Sicilian mountain top; this shows that I am not even a molecular biologist. In fact, the list of what I have not got makes up the American Dream. Readers, if any, will conclude rightly that the Gradus ad Parnassum will have to be learned at somebody else’s feet.

I do not find that any one has doubted that there are four elements. The highest of these is supposed to be fire, and hence proceed the eyes of so many glittering stars. The next is that spirit, which both the Greeks and ourselves call by the same name, air. It is by the force of this vital principle, pervading all things and mingling with all, that the earth, together with the fourth element, water, is balanced in the middle of space.

I have considered the two terms you want to substitute for eisode and exode, and upon the whole I am disposed to recommend instead of them anode and cathode. These words may signify eastern and western way, just as well as the longer compounds which you mention … I may mention too that anodos and cathodos are good, genuine Greek words, and not compounds coined for the purpose.

I have often thought that an interesting essay might be written on the influence of race on the selection of mathematical methods. methods. The Semitic races had a special genius for arithmetic
and algebra, but as far as I know have never produced a single geometrician of any eminence. The Greeks on the other hand adopted a geometrical procedure wherever it was possible, and they even treated arithmetic as a branch of geometry by means of the device of representing numbers by lines.

I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the “Law of Frequency of Error.” The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand and marshaled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.

I must confess the language of symbols is to meA Babylonish dialectWhich learned chemists much affect;It is a party-coloured dressOf patch'd and piebald languages:'T is English cut on Greek and Latin,Like fustian heretofore on satin.

I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.

I wish they would use English instead of Greek words. When I want to know why a leaf is green, they tell me it is coloured by “chlorophyll,” which at first sounds very instructive; but if they would only say plainly that a leaf is coloured green by a thing which is called “green leaf,” we should see more precisely how far we had got.

If atoms do, by chance, happen to combine themselves into so many shapes, why have they never combined together to form a house or a slipper? By the same token, why do we not believe that if innumerable letters of the Greek alphabet were poured all over the market-place they would eventually happen to form the text of the Iliad?

If the views we have ventured to advance be correct, we may almost consider {greek words} of the ancients to be realised in hydrogen, an opinion, by the by, not altogether new. If we actually consider the specific gravities of bodies in their gaseous state to represent the number of volumes condensed into one; or in other words, the number of the absolute weight of a single volume of the first matter ({greek words}) which they contain, which is extremely probable, multiples in weight must always indicate multiples in volume, and vice versa; and the specific gravities, or absolute weights of all bodies in a gaseous state, must be multiples of the specific gravity or absolute weight of the first matter, ({Greek words}), because all bodies in the gaseous state which unite with one another unite with reference to their volume.

If we compare a mathematical problem with an immense rock, whose interior we wish to penetrate, then the work of the Greek mathematicians appears to us like that of a robust stonecutter, who, with indefatigable perseverance, attempts to demolish the rock gradually from the outside by means of hammer and chisel; but the modern mathematician resembles an expert miner, who first constructs a few passages through the rock and then explodes it with a single blast, bringing to light its inner treasures.

If we look at the problems raised by Aristotle, we are astonished at his gift of observation. What wonderful eyes the Greeks had for many things! Only they committed the mistake of being overhasty, of passing straightway from the phenomenon to the explanation of it, and thereby produced certain theories that are quite inadequate. But this is the mistake of all times, and still made in our own day.

In science, attempts at formulating hierarchies are always doomed to eventual failure. A Newton will always be followed by an Einstein, a Stahl by a Lavoisier; and who can say who will come after us? What the human mind has fabricated must be subject to all the changes—which are not progress—that the human mind must undergo. The 'last words' of the sciences are often replaced, more often forgotten. Science is a relentlessly dialectical process, though it suffers continuously under the necessary relativation of equally indispensable absolutes. It is, however, possible that the ever-growing intellectual and moral pollution of our scientific atmosphere will bring this process to a standstill. The immense library of ancient Alexandria was both symptom and cause of the ossification of the Greek intellect. Even now I know of some who feel that we know too much about the wrong things.

In the beginning was the myth. God, in his search for self-expression, invested the souls of Hindus, Greeks, and Germans with poetic shapes and continues to invest each child’s soul with poetry every day.

In the history of physics, there have been three great revolutions in thought that first seemed absurd yet proved to be true. The first proposed that the earth, instead of being stationary, was moving around at a great and variable speed in a universe that is much bigger than it appears to our immediate perception. That proposal, I believe, was first made by Aristarchos two millenia ago ... Remarkably enough, the name Aristarchos in Greek means best beginning.[The next two revolutions occurred ... in the early part of the twentieth century: the theory of relativity and the science of quantum mechanics...]

It is interesting to note how many fundamental terms which the social sciences are trying to adopt from physics have as a matter of historical fact originated in the social field. Take, for instance, the notion of cause. The Greek aitia or the Latin causa was originally a purely legal term. It was taken over into physics, developed there, and in the 18th century brought back as a foreign-born kind for the adoration of the social sciences. The same is true of the concept of law of nature. Originally a strict anthropomorphic conception, it was gradually depersonalized or dehumanized in the natural sciences and then taken over by the social sciences in an effort to eliminate final causes or purposes from the study of human affairs. It is therefore not anomalous to find similar transformations in the history of such fundamental concepts of statistics as average and probability. The concept of average was developed in the Rhodian laws as to the distribution of losses in maritime risks. After astronomers began to use it in correcting their observations, it spread to other physical sciences; and the prestige which it thus acquired has given it vogue in the social field. The term probability, as its etymology indicates, originates in practical and legal considerations of probing and proving.

It is not necessary to probe into the nature of things, as was done by those whom the Greeks call physici; nor need we be in alarm lest the Christian should be ignorant of the force and number of the elements—the motion, and order, and eclipses of the heavenly bodies; the form of the heavens; the species and the natures of animals, plants, stones, fountains, rivers, mountains; about chronology and distances; the signs of coming storms; and a thousand other things which those philosophers either have found out, or think they have found out. … It is enough for the Christian to believe that the only cause of all created things, whether heavenly or earthly … is the goodness of the Creator, the one true God.

In Marcus Dods (ed.), J.F. Shaw (trans.), The Enchiridion of Augustine, Chap. 9, collected in The Works of Aurelius Augustine, Bishop of Hippo: A new translation (1873), Vol. 9, 180-181. The physici are natural philosophers.

It is not, indeed, strange that the Greeks and Romans should not have carried ... any ... experimental science, so far as it has been carried in our time; for the experimental sciences are generally in a state of progression. They were better understood in the seventeenth century than in the sixteenth, and in the eighteenth century than in the seventeenth. But this constant improvement, this natural growth of knowledge, will not altogether account for the immense superiority of the modern writers. The difference is a difference not in degree, but of kind. It is not merely that new principles have been discovered, but that new faculties seem to be exerted. It is not that at one time the human intellect should have made but small progress, and at another time have advanced far; but that at one time it should have been stationary, and at another time constantly proceeding. In taste and imagination, in the graces of style, in the arts of persuasion, in the magnificence of public works, the ancients were at least our equals. They reasoned as justly as ourselves on subjects which required pure demonstration.

It is possible that the deepest meaning and aim of Newtonianism, or rather, of the whole scientific revolution of the seventeenth century, of which Newton is the heir and the highest expression, is just to abolish the world of the 'more or less', the world of qualities and sense perception, the world of appreciation of our daily life, and to replace it by the (Archimedean) universe of precision, of exact measures, of strict determination ... This revolution [is] one of the deepest, if not the deepest, mutations and transformations accomplished—or suffered—by the human mind since the invention of the cosmos by the Greeks, two thousand years before.

It is said that Thales of Miletus, who was the first of the Greeks to devote himself to the study of the stars, was on one occasion so intent upon observing the heavens that he fell into a well, whereupon a maidservant laughed and remarked, “In his zeal for things in the sky he does
not see what is at his feet.”

From an essay concerning the Regius Professorship of Greek, The New Method of Evaluating as Applied to π (1865), as quoted and cited in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 159. Collingwood explains parenthetically, after "result J", “[i.e., Jowett]”, which was not in the original publication of “The New Method…”.

Man is a rational animal—so at least I have been told. … Aristotle, so far as I know, was the first man to proclaim explicitly that man is a rational animal. His reason for this view was … that some people can do sums. … It is in virtue of the intellect that man is a rational animal. The intellect is shown in various ways, but most emphatically by mastery of arithmetic. The Greek system of numerals was very bad, so that the multiplication table was quite difficult, and complicated calculations could only be made by very clever people.

Man is the Reasoning Animal. Such is the claim. I think it is open to dispute. Indeed, my experiments have proven to me that he is the Unreasoning Animal. Note his history, as sketched above. It seems plain to me that whatever he is he is not a reasoning animal. His record is the fantastic record of a maniac. I consider that the strongest count against his intelligence is the fact that with that record back of him he blandly sets himself up as the head animal of the lot: whereas by his own standards he is the bottom one.In truth, man is incurably foolish. Simple things which the other animals easily learn, he is incapable of learning. Among my experiments was this. In an hour I taught a cat and a dog to be friends. I put them in a cage. In another hour I taught them to be friends with a rabbit. In the course of two days I was able to add a fox, a goose, a squirrel and some doves. Finally a monkey. They lived together in peace; even affectionately.Next, in another cage I confined an Irish Catholic from Tipperary, and as soon as he seemed tame I added a Scotch Presbyterian from Aberdeen. Next a Turk from Constantinople; a Greek Christian from Crete; an Armenian; a Methodist from the wilds of Arkansas; a Buddhist from China; a Brahman from Benares. Finally, a Salvation Army Colonel from Wapping. Then I stayed away two whole days. When I came back to note results, the cage of Higher Animals was all right, but in the other there was but a chaos of gory odds and ends of turbans and fezzes and plaids and bones and flesh—not a specimen left alive. These Reasoning Animals had disagreed on a theological detail and carried the matter to a Higher Court.

Marx founded a new science: the science of history. … The sciences we are familiar with have been installed in a number of great “continents”. Before Marx, two such continents had been opened up to scientific knowledge: the continent of Mathematics and the continent of Physics. The first by the Greeks (Thales), the second by Galileo. Marx opened up a third continent to scientific knowledge: the continent of History.

Mathematics as a science commenced when first someone, probably a Greek, proved propositions about any things or about some things, without specification of definite particular things. These propositions were first enunciated by the Greeks for geometry; and, accordingly, geometry was the great Greek mathematical science.

Mathematics will not be properly esteemed in wider circles until more than the a b c of it is taught in the schools, and until the unfortunate impression is gotten rid of that mathematics serves no other purpose in instruction than the formal training of the mind. The aim of mathematics is its content, its form is a secondary consideration and need not necessarily be that historic form which is due to the circumstance that mathematics took permanent shape under the influence of Greek logic.

Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.

Medicine is essentially a learned profession. Its literature is ancient, and connects it with the most learned periods of antiquity; and its terminology continues to be Greek or Latin. You cannot name a part of the body, and scarcely a disease, without the use of a classical term. Every structure bears upon it the impress of learning, and is a silent appeal to the student to cultivate an acquaintance with the sources from which the nomenclature of his profession is derived.

From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 11.

Much later, when I discussed the problem with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life. But this “blunder,” rejected by Einstein, is still sometimes used by cosmologists even today, and the cosmological constant denoted by the Greek letter Λ rears its ugly head again and again and again.

My World Line (1970). Cited in Edward Robert Harrison, Cosmology: the Science of the Universe (2000), 379, which adds: “The Λ force is referred to by various names, such as the cosmological constant, cosmological term, cosmical constant or cosmical term.”

One dictionary that I consulted remarks that “natural history” now commonly means the study of animals and plants “in a popular and superficial way,” meaning popular and superficial to be equally damning adjectives. This is related to the current tendency in the biological sciences to label every subdivision of science with a name derived from the Greek. “Ecology” is erudite and profound; while “natural history” is popular and superficial. Though, as far as I can see, both labels apply to just about the same package of goods.

One striking peculiarity of mathematics is its unlimited power of evolving examples and problems. A student may read a book of Euclid, or a few chapters of Algebra, and within that limited range of knowledge it is possible to set him exercises as real and as interesting as the propositions themselves which he has studied; deductions which might have pleased the Greek geometers, and algebraic propositions which Pascal and Fermat would not have disdained to investigate.

Our science, in contrast with others, is not founded on a single period of human history, but has accompanied the development of culture through all its stages. Mathematics is as much interwoven with Greek culture as with the most modern problems in Engineering. She not only lends a hand to the progressive natural sciences but participates at the same time in the abstract investigations of logicians and philosophers.

Petr Beckmann has divided the men who made history into two classes, the thinkers and the thugs. The Greeks were the thinkers and the Romans were the thugs. The general law seems to be that the thugs always win, but the thinkers always outlive them.

In Mathematical Circles Squared (1972), 153. Petr Beckman wrote: “150 years saw the confrontation of Athens and Sparta, the thinkers against the thugs. The thugs always win, but the thinkers always outlast them”, in A History of Pi (1970), 34.

Physicists are, as a general rule, highbrows. They think and talk in long, Latin words, and when they write anything down they usually include at least one partial differential and three Greek letters.

Sarcophagus is a stone that devours dead bodies, for in Greek σάρκος means “flesh” and φαγώ “eating”. Some of the ancients first made coffins for the dead of this stone because in the space of thirty days it consumed the dead… . For this reason stone monuments are called sarcophagi.

Saturated with that speculative spirit then pervading the Greek mind, he [Pythagoras] endeavoured to discover some principle of homogeneity in the universe. Before him, the philosophers of the Ionic school had sought it in the matter of things; Pythagoras looked for it in the structure of things. He observed the various numerical relations or analogies between numbers and the phenomena of the universe. Being convinced that it was in numbers and their relations that he was to find the foundation to true philosophy, he proceeded to trace the origin of all things to numbers. Thus he observed that musical strings of equal lengths stretched by weights having the proportion of 1/2, 2/3, 3/4, produced intervals which were an octave, a fifth and a fourth. Harmony, therefore, depends on musical proportion; it is nothing but a mysterious numerical relation. Where harmony is, there are numbers. Hence the order and beauty of the universe have their origin in numbers. There are seven intervals in the musical scale, and also seven planets crossing the heavens. The same numerical relations which underlie the former must underlie the latter. But where number is, there is harmony. Hence his spiritual ear discerned in the planetary motions a wonderful “Harmony of spheres.”

Science only means knowledge; and for [Greek] ancients it did only mean knowledge. Thus the favorite science of the Greeks was Astronomy, because it was as abstract as Algebra. ... We may say that the great Greek ideal was to have no use for useful things. The Slave was he who learned useful things; the Freeman was he who learned useless things. This still remains the ideal of many noble men of science, in the sense they do desire truth as the great Greeks desired it; and their attitude is an external protest against vulgarity of utilitarianism.

Scientists come in two varieties, hedgehogs and foxes. I borrow this terminology from Isaiah Berlin (1953), who borrowed it from the ancient Greek poet Archilochus. Archilochus told us that foxes know many tricks, hedgehogs only one. Foxes are broad, hedgehogs are deep. Foxes are interested in everything and move easily from one problem to another. Hedgehogs are only interested in a few problems that they consider fundamental, and stick with the same problems for years or decades. Most of the great discoveries are made by hedgehogs, most of the little discoveries by foxes. Science needs both hedgehogs and foxes for its healthy growth, hedgehogs to dig deep into the nature of things, foxes to explore the complicated details of our marvelous universe. Albert Einstein and Edwin Hubble were hedgehogs. Charley Townes, who invented the laser, and Enrico Fermi, who built the first nuclear reactor in Chicago, were foxes.

Seeing and thinking have done much for human progress; in the sphere of mind and morals everything, and could the world have been saved by armchair philosophy, the Greeks would have done it; but only a novum organon could do this, the powerful possibilities of which were only revealed when man began to search our the secrets of nature by way of experiment, to use the words of Harvey.

Address at the opening of the new Pathological Institute of the Royal Infirmary, Glasgow (4 Oct 1911). Printed in 'The Pathological Institute of a General Hospital', Glasgow Medical Journal (1911), 76, 326.

Since it is necessary for specific ideas to have definite and consequently as far as possible selected terms, I have proposed to call substances of similar composition and dissimilar properties isomeric, from the Greek ίσομερης (composed of equal parts).

The discovery of the famous original [Rosetta Stone] enabled Napoleon’s experts to begin the reading of Egypt’s ancient literature. In like manner the seismologists, using the difficult but manageable Greek of modern physics, are beginning the task of making earthquakes tell the nature of the earth’s interior and translating into significant speech the hieroglyphics written by the seismograph.

The future science of government should be called “la cybernétique” (1843)Coining the French word to mean “the art of governing,” from the Greek (Kybernetes = navigator or steersman), subsequently adopted as cybernetics by Norbert Weiner for the field of control and communication theory.

The geometrical problems and theorems of the Greeks always refer to definite, oftentimes to rather complicated figures. Now frequently the points and lines of such a figure may assume very many different relative positions; each of these possible cases is then considered separately. On the contrary, present day mathematicians generate their figures one from another, and are accustomed to consider them subject to variation; in this manner they unite the various cases and combine them as much as possible by employing negative and imaginary magnitudes. For example, the problems which Apollonius treats in his two books De sectione rationis, are solved today by means of a single, universally applicable construction; Apollonius, on the contrary, separates it into more than eighty different cases varying only in position. Thus, as Hermann Hankel has fittingly remarked, the ancient geometry sacrifices to a seeming simplicity the true simplicity which consists in the unity of principles; it attained a trivial sensual presentability at the cost of the recognition of the relations of geometric forms in all their changes and in all the variations of their sensually presentable positions.

The Good Spirit never cared for the colleges, and though all men and boys were now drilled in Greek, Latin, and Mathematics, it had quite left these shells high on the beach, and was creating and feeding other matters [science] at other ends of the world.

The Greeks are wrong to recognize coming into being and perishing; for nothing comes into being nor perishes, but is rather compounded or dissolved from things that are. So they would be right to call coming into being composition and perishing dissolution.

The Greeks have given us one of the most beautiful words of our language, the word “enthusiasm” – a God within. The grandeur of the acts of men is measured by the inspiration from which they spring. Happy is he who bears a God within!

The Greeks in the first vigour of their pursuit of mathematical truth, at the time of Plato and soon after, had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature; but had followed out many beautiful trains of research concerning various kinds of figures, for the sake of their beauty alone; as for instance in their doctrine of Conic Sections, of which curves they had discovered all the principal properties. But it is curious to remark, that these investigations, thus pursued at first as mere matters of curiosity and intellectual gratification, were destined, two thousand years later, to play a very important part in establishing that system of celestial motions which succeeded the Platonic scheme of cycles and epicycles. If the properties of conic sections had not been demonstrated by the Greeks and thus rendered familiar to the mathematicians of succeeding ages, Kepler would probably not have been able to discover those laws respecting the orbits and motions of planets which were the occasion of the greatest revolution that ever happened in the history of science.

The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science “more geometrico.”

The history of Europe is the history of Rome curbing the Hebrew and the Greek, with their various impulses of religion, and of science, and of art, and of quest for material comfort, and of lust of domination, which are all at daggers drawn with each other. The vision of Rome is the vision of the unity of civilisation.

The rise of every man he loved to trace,Up to the very pod O!And, in baboons, our parent raceWas found by old Monboddo.Their A, B, C, he made them speak.And learn their qui, quæ, quod, O!Till Hebrew, Latin, Welsh, and GreekThey knew as well’s Monboddo!

From Ballad, 'The Memory of Monboddo', in Blackwood’s Magazine (Sep 1861), 90, No. 551, 363, Verse 2 (of 6). Written to the Air, The Looking Glass. It is footnoted to explain that Lord (James Burnett) Monboddo “has written a book about the origin of language, in which he traces monkeys up to men.” The note is quoted and cited from Boswell’s Life of Johnson, Vol. 4, 73.

The school of Plato has advanced the interests of the race as much through geometry as through philosophy. The modern engineer, the navigator, the astronomer, built on the truths which those early Greeks discovered in their purely speculative investigations. And if the poetry, statesmanship, oratory, and philosophy of our day owe much to Plato’s divine Dialogues, our commerce, our manufactures, and our science are equally indebted to his Conic Sections. Later instances may be abundantly quoted, to show that the labors of the mathematician have outlasted those of the statesman, and wrought mightier changes in the condition of the world. Not that we would rank the geometer above the patriot, but we claim that he is worthy of equal honor.

The story is told of Lord Kelvin, a famous Scotch physicist of the last century, that after he had given a lecture on atoms and molecules, one of his students came to him with the question, “Professor, what is your idea of the structure of the atom.”“What,” said Kelvin, “The structure of the atom? Why, don’t you know, the very word ‘atom’ means the thing that can’t be cut. How then can it have a structure?”“That,” remarked the facetious young man, “shows the disadvantage of knowing Greek.”

The word “mathematics” is a Greek word and, by origin, it means “something that has been learned or understood,” or perhaps “acquired knowledge,” or perhaps even, somewhat against grammar, “acquirable knowledge,” that is, “learnable knowledge,” that is, “knowledge acquirable by learning.”

There are reported to be six species of metals, namely, gold, silver, iron, copper, tin, and lead. Actually there are more. Mercury is a metal although we differ on this point with the chemists. Plumbum cinereum (gray lead) which we call bisemutum was unknown to the older Greek writers. On the other hand, Ammonius writes correctly many metals are unknown to us, as well as many plants and animals.

As translated by Mark Chance Bandy and Jean A. Bandy from the first Latin Edition of 1546 in De Natura Fossilium: (Textbook of Mineralogy) (2004), 19. Originally published by Geological Society of America as a Special Paper (1955). There are other translations with different wording.

There are some arts which to those that possess them are painful, but to those that use them are helpful, a common good to laymen, but to those that practise them grievous. Of such arts there is one which the Greeks call medicine. For the medical man sees terrible sights, touches unpleasant things, and the misfortunes of others bring a harvest of sorrows that are peculiarly his; but the sick by means of the art rid themselves of the worst of evils, disease, suffering, pain and death.

There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.

They think that differential equations are not reality. Hearing some colleagues speak, it’s as though theoretical physics was just playing house with plastic building blocks. This absurd idea has gained currency, and now people seem to feel that theoretical physicists are little more than dreamers locked away ivory towers. They think our games, our little houses, bear no relation to their everyday worries, their interests, their problems, or their welfare. But I’m going to tell you something, and I want you to take it as a ground rule for this course. From now on I will be filling this board with equations. … And when I'm done, I want you to do the following: look at those numbers, all those little numbers and Greek letters on the board, and repeat to yourselves, “This is reality,” repeat it over and over.

To find fault with our ancestors for not having annual parliaments, universal suffrage, and vote by ballot, would be like quarrelling with the Greeks and Romans for not using steam navigation, when we know it is so safe and expeditious; which would be, in short, simply finding fault with the third century before Christ for not being the eighteenth century after. It was necessary that many other things should be thought and done, before, according to the laws of human affairs, it was possible that steam navigation should be thought of. Human nature must proceed step by step, in politics as well as in physics.

Very little of Roman literature will find its way into the kingdom of heaven, when the events of this world will have lost their importance. The languages of heaven will be Chinese, Greek, French, German, Italian, and English, and the blessed Saints will dwell with delight on these golden expressions of eternal life. They will be wearied with the moral fervour of Hebrew literature in its battle with a vanished evil, and with Roman authors who have mistaken the Forum for the footstool of the living God.

We have decided to call the entire field of control and communication theory, whether in the machine or in the animal, by the name Cybernetics, which we form from the Greek … for steersman. In choosing this term, we wish to recognize that the first significant paper on feedback mechanisms is an article on governors, which was published by Clerk Maxwell in 1868, and that governor is derived from a Latin corruption … We also wish to refer to the fact that the steering engines of a ship are indeed one of the earliest and best-developed forms of feedback mechanisms.

We might call it the transformational content of the body … But as I hold it better to borrow terms for important magnitudes from the ancient languages, so that they may be adopted unchanged in all modern languages, I propose to call [it] the entropy of the body, from the Greek word “trope” for “transformation” I have intentionally formed the word “entropy” to be as similar as possible to the word “energy”; for the two magnitudes to be denoted by these words are so nearly allied in their physical meanings, that a certain similarity in designation appears to be desirable.

We need a name for the new replicator, a noun that conveys the idea of a unit of cultural transmission, or a unit of imitation. 'Mimeme' comes from a suitable Greek root, but I want a monosyllable that sounds a bit like 'gene'. I hope my classicist friends will forgive me if I abbreviate mimeme to meme. If it is any consolation, it could alternatively be thought of as being related to 'memory', or to the French word même. It should be pronounced to rhyme with 'cream'.

What marvel is this? We begged you for drinkable springs,O earth, and what is your lap sending forth?Is there life in the deeps as well? A race yet unknownHiding under the lava? Are they who had fled returning?Come and see, Greeks; Romans, come! Ancient Pompeii Is found again, the city of Hercules rises!

Translation as given, without citation, as epigraph in C.W. Ceram, Gods, Graves, and Scholars: The Story of Archaeology (1986), 1. There are other translations of the Schiller’s original German, for example, in 'Pompeii and Herculaneum', Life of Schiller: Poetical Works (1902), 249.

What strange wonder is this? Our prayer to thee was for water,Earth! What is this that thou now send’st from thy womb in reply?In the abyss is there life ? Or hidden under the lavaDwelleth some race now unknown? Does what hath fled e’er return?Greeks and Romans, oh come! Oh, see the ancient PompeiiHere is discover’d again,—Hercules’ town is rebuilt!

Whatever we Greeks receive from the barbarians, we improve and perfect; there is good hope and promise, therefore that Greeks will carry this knowledge far beyond that which was introduced from abroad.

From the 'Epilogue to the Laws' (Epinomis). As quoted in William Whewell, History of the Inductive Sciences from the Earliest to the Present Time (1837), Vol. 1, 161. (Although referenced to Plato’s Laws, the Epinomis is regarded as a later addition, not by Plato himself.)

Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last fifty years.

[King Hiero II] requested Archimedes to consider [whether a crown was pure gold or alloyed with silver]. The latter, while the case was still on his mind, happened to go to the bath, and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. As this pointed out the way to explain the case in question, without a moment’s delay, and transported with joy, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for as he ran he shouted repeatedly in Greek, “Eὕρηκα, εὕρηκα.”

This famous anecdote, being written about two centuries after Archimedes, is of questionable authenticity, but Vitruvius provided the origin of the story as we know it. In De Architectura, Book 9, Introduction, Sec. 10. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 254. Also seen translated as “While Archimedes was turning the problem over, he chanced to come to the place of bathing, and there, as he was sitting down in the tub, he noticed that the amount of water which flowed over the tub was equal to the amount by which his body was immersed. This showed him a means of solving the problem. … In his joy, he leapt out of the tub and, rushing naked towards his home, he cried out with a loud voice that he had found what he sought.” In Ivor Bulmer-Thomas, Selections Illustrating the History of Greek Mathematics (1939), 37.

[L]et us not overlook the further great fact, that not only does science underlie sculpture, painting, music, poetry, but that science is itself poetic. The current opinion that science and poetry are opposed is a delusion. ... On the contrary science opens up realms of poetry where to the unscientific all is a blank. Those engaged in scientific researches constantly show us that they realize not less vividly, but more vividly, than others, the poetry of their subjects. Whoever will dip into Hugh Miller's works on geology, or read Mr. Lewes's “Seaside Studies,” will perceive that science excites poetry rather than extinguishes it. And whoever will contemplate the life of Goethe will see that the poet and the man of science can co-exist in equal activity. Is it not, indeed, an absurd and almost a sacrilegious belief that the more a man studies Nature the less he reveres it? Think you that a drop of water, which to the vulgar eye is but a drop of water, loses anything in the eye of the physicist who knows that its elements are held together by a force which, if suddenly liberated, would produce a flash of lightning? Think you that what is carelessly looked upon by the uninitiated as a mere snow-flake, does not suggest higher associations to one who has seen through a microscope the wondrously varied and elegant forms of snow-crystals? Think you that the rounded rock marked with parallel scratches calls up as much poetry in an ignorant mind as in the mind of a geologist, who knows that over this rock a glacier slid a million years ago? The truth is, that those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded. Whoever has not in youth collected plants and insects, knows not half the halo of interest which lanes and hedge-rows can assume. Whoever has not sought for fossils, has little idea of the poetical associations that surround the places where imbedded treasures were found. Whoever at the seaside has not had a microscope and aquarium, has yet to learn what the highest pleasures of the seaside are. Sad, indeed, is it to see how men occupy themselves with trivialities, and are indifferent to the grandest phenomena—care not to understand the architecture of the Heavens, but are deeply interested in some contemptible controversy about the intrigues of Mary Queen of Scots!—are learnedly critical over a Greek ode, and pass by without a glance that grand epic written by the finger of God upon the strata of the Earth!

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan